Abstract
Ensemble prediction systems (EPSs) are usually validated under the assumption that the verifying observations are exact. In this paper, two methods are considered for taking observation errors into account. In the ‘perturbed‐ensemble’ method, which has already been studied by other authors, the predicted ensemble elements are randomly perturbed in a way that is consistent with the assumed observation error. In the ‘observational‐probability’ method, which is new, a verifying observation is considered as defining, together with the assumed associated error, a probability distribution. All standard scores for evaluation of EPSs (reliability diagram, Brier score, ranked probability score (RPS), continuous RPS (CRPS), relative‐operating‐characteristics (ROC) curve area), with the exception of the rank histogram, remain defined in this second method. In particular, the classical reliability–resolution decomposition of the Brier score, and of its extension to the RPS and CRPS, remain defined.
Numerical simulations, partially supported by theoretical considerations, show that, with respect to the case when observation errors are ignored, the perturbed‐ensemble method improves reliability, as well as the ROC score, while it has no significant impact on resolution, as measured by the Brier score. The observational‐probability method, on the other hand, degrades reliability and the ROC score, but improves resolution.
With respect to the ‘real’ performance of the system (i.e. the one that would be diagnosed if no error were present), reliability is unchanged in the perturbed‐ensemble method, while resolution and the ROC score are degraded. The observational‐probability method degrades reliability and the ROC score. As for resolution, an optimum value of the observational error is found, below which resolution is improved.
Diagnostics performed on the operational EPS of the Canadian Meteorological Centre confirm the results of the simulations as to the consequences of ignoring observation errors, or on the contrary of taking them into account through either of the two methods. The significance of those various results is discussed. This article replaces a previously published version (Q. J. R. Meteorol. Soc. 134(631): 509–521, DOI: 10.1002/qj.221). Copyright © 2008 Royal Meteorological Society